1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
tigry1 [53]
3 years ago
15

verify that the fucntion satisfies the three hypotheses of rolles theorem on the given interval . then find all numbers c that s

atisfy the conclusion . f(x)= x^3-2x^2-4x+2 . [ -2,2]
Mathematics
1 answer:
Ghella [55]3 years ago
4 0

The roots of the polynomial <span><span>x^3 </span>− 2<span>x^2 </span>− 4x + 2</span> are:

<span><span>x1 </span>= 0.42801</span>

<span><span>x2 </span>= −1.51414</span>

<span><span>x3 </span>= 3.08613</span>


x1 and x2 are in the desired interval [-2, 2]

f'(x) = 3x^2 - 4x - 4

so we have:

3x^2 - 4x - 4 = 0

<span>x = ( 4 +- </span><span>√(16 + 48) </span>)/6

x_1 = -4/6 = -0.66

x_ 2 = 2

According to Rolle's theorem, we have one point in between:

x1 = 0.42801 and x2 = −1.51414

where f'(x) = 0, and that is <span>x_1 = -0.66</span>

so we see that Rolle's theorem holds in our function.

You might be interested in
For the given angle 0, identify the reference angle, _
ankoles [38]

Answer:

π\6

Step-by-step explanation:

The reference angle is the smallest angle measured from the terminal side of the angle (where the angle ends) to the x axis. The reference angle is an acute angle (i.e less than 90° or π/2)

For O = 11π/6 = 1.833π

1.833π is in the fourth quadrant between 3π/2 radians and 2π radians. Since it is in the fourth quadrant, the reference angle is given as:

reference angle = 2π - 11π/6 = π\6

5 0
3 years ago
What is the surface area?<br><br> 2 mm<br> 2 mm<br> 2 mm<br><br> square millimeters
Alona [7]

Answer:

24 mm^2

Step-by-step explanation:

length x width x 6 sides in a cube

(2)(2)(6)=24

4 0
3 years ago
Please Answer<br> 6. Find mABC <br> 7. If mPQ =(5x +17)° , find x. <br> 8. Find m∠1
lys-0071 [83]

Answer:

The answer is

252

25.4

125

7 0
2 years ago
• The ratio of cookies to eggs was 9 to
UkoKoshka [18]
I got shot in the Hebrew morning I was going on the same day lol I was going on the balls in
4 0
2 years ago
Determine the cost per pound:<br> 313 pounds of apples for $10.50
Misha Larkins [42]

Answer:

3 cents

Step-by-step explanation:

Divide the cost by total pounds. 10.5 divided by 313 is 0.03.

6 0
2 years ago
Other questions:
  • Help please!! I’ll give brainliest.....
    7·2 answers
  • PLEASE HELP IM SO STUCK 20 POINTS
    10·1 answer
  • A survey finds that 40% of students ride in a car to school. Eri would like to estimate the probability that if 3 students were
    14·2 answers
  • Analyze the graph and determine the most
    15·2 answers
  • How many solutions does the following system of equations have?<br> 2y= 5x + 4<br> 1 = 3x + 2
    6·1 answer
  • What is the area of this parallelogram? 10.35 cm² 12.5 cm² 20.25 cm² 30.6 cm² Parallelogram A B C D is composed of a square and
    9·2 answers
  • How do I do algebra
    5·1 answer
  • The city sales tax in your city is 4.4% and an item costs $3 before tax
    11·1 answer
  • !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    9·2 answers
  • Write an equation and solve for x
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!